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Question

How do you find diameter from the circumference of a circle?


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Solution

Step 1: Define the diameter and the circumference of a circle:

The diameter is the longest chord of a circle that passes through the center. The diameter of a circle is double its radius, i.e., D=2r.

The perimeter of a circle is called the circumference of a circle. It is defined by the formula C=2πr.

Step 2: Calculate the diameter from the circumference

Since, D=2r

r=D2 …(i)

Now, if it is known that C=2πr …(ii)

Using equation (i) in the equation (ii), we get,

C=2π×D2

C=π×D

C=πDD=πC

the above formula can be used to calculate diameter if the circumference is known.

Hence, the diameter from the circumference of a circle can be calculated using the formula D=πC.


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